You could use either the present or the past here. Grammar usually say to use the past in situations like this. This is not reported speech, but it is possible to report what one thinks. Let's call it reported thoughts.
Here's how we justify using either past or present:
past - If the reporting verb is the past, then it follows that the next verb should be a past form.
present - If the reporting verb is the past, but what one is reporting is a statement of fact or truth in the present, then it makes sense to use the present after the reporting verb even if the reporting verb is a past tense verb. This doesn't always work out well, but it often does. It depends on the sentence.
Here's what I think about your example sentences:
I thought the bus leaves/left at 8. - To me, it makes sense to use either "leaves" or "left" if you are talking about a bus schedule.
I thought the guy was/is dead. - Here I would use only "was".
I thought the rule only applies to employees. - To me, it makes sense to use either "applies" or "applied".
applies: It's okay to use applies because you are referring to that which could be based on fact or the truth.
applied: It's okay to use "applied" because it is preceded by "thought", which is the reporting verb.
Another example:
She said her name was Claudia. - And it is, but "was" follows "said".
She said her name is Claudia. - And it still is her name. Therefore, it makes sense to use "is".
